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Explain why the high-risk types will always purchase insurance at the zero-profit price. Given that high risk types always purchase insurance, we are interested in when it is an equilibrium for low risk types to get insurance as well. If the insurance company expects both types to get insurance, what is the zero-profit price p* she charges? (p* depends on q, pi_H, pi_l and C). Given the zero-profit price p*, what is the low risk type’s utility when buying insurance, when not buying insurance? When is the low risk type better off buying the insurance? What is the maximum value C* of C such that low risk types choose to buy insurance? We now study when it is an equilibrium for low risk types not to buy insurance. If the insurance company expects that only high risk types get insurance, what is the zero-profit price she charges? Do low risk types want to purchase insurance at this price? Depending on C, what are the possible equilibrium? Consider the case where pi_l = .1, pih = .5, 5 = 2000, q = .8 and, initially, C = 1000. What is the value of C*? Is there an equilibrium in which low risk types get insurance? Say that initially, when C = 1000, we are in the good equilibrium where low risk types get insurance. Imagine that because of a change in medical practices, the cost of treatment rises to C= 1500. What are the possible equilibrium at this price? Is this an efficient outcome? Now imagine that the government puts pressure on hospitals to become more efficient so that the cost of treatment goes back to C = 1000. Is it clear that the system will go back to the original good equilibrium? We explore two strategies that the government could use to push the system back to the good equilibrium. Strategy 1 is to force everybody to buy insurance. Strategy 2 is to subsidize the cost of insurance by an amount s, so that if the insurance company charges price p, the consumer only pays an amount p – s. Explain why strategy 1 would push the system back to the good equilibrium (no algebra). We now turn to strategy 2. Using your answer to question (d), show that the insurance company will always charge a price p lessthanorequalto 500. Show that if s > 300, then low types will want to buy insurance and the system will go back to the original equilibrium. Which strategy is costlier for the state? Which strategy respects individual freedom the most? Depending on whether the state is running a large deficit or a large surplus, which strategy is most appropriate to push the health system back to the good equilibrium?

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